An evolving system is comprised of a huge collection of entities that interact locally. The rules governing these local interactions change over time by means of natural selection, and the result of natural selection is the production of adaptation. A fundamental open question in the study of evoving systems is whether there are quantitative laws that characterize adaptive evolution in large classes of evolving systems. The first step toward such laws would be a "zeroth" law (analogous to the zeroth law in thermodynamics) which would state that it is possible to make quantitative comparisons about the dynamics of adaptive evolution across different evolving systems. This talk presents new progress toward such a zeroth law. Measuerments of the extent and intensity of the process of adaptive evolution are explained and illustrated in a variety of artificial and natural evolving systems. One conclusion of these quantitative comparisons is a 4-fold classification of evolving systems.